Distortion compensator



Feb. 12, 1929.

O. J. ZOBEL DISTORTION COMPENSATOR Filed June 26, .1924

2 Sheets-Sheet INVENTOR O. J Zae A TTORNEY Feb. '12, 1929..

x o. J. ZOBEL DISTORTICON COMPENSATOR Fi led June 26, 1924 2 Sheets-Sheet Time b'n/ seconds INVENTOR JZaafi A TTORNE Y OTTO J. ZOBEL, O

Patented Feb. 12, 1929. A

UNITED STATES PATENT OFFICE.

F NEW YORK, N. Y., ASSIGNOR TO AMERICA N TELEPHONE AND TELE- GRAPH COMPANY, A CORPORATION OF NEW YORK.

msron'rion GOMPENSA'IOR? Application filed June .26,

Anobject of my invention is to provide a new and improved electrical transmission system in which the frequency components of the current within acertain desired frequency range will be in the same phase relation with one another at the receiving end as at the transmitting end. Another object of my. invention is to make the received composite wave form in such a system of the same shape shift on the line and to restore the components at the receiving end of the line to the same phase 'relation as at the sending end. Still another object is to provide a transducer at the receiving .end of a transmission line that shall compensate the distortion due to diflerential phase shift and differential attenuation on the line.

By the term transducer, as employed in "this specification, I mean to refer to any apparatus having a pair of input terminls for the application of an electromotive force and a pai1of output terminals by which electroinvention.

theappen'd'ed claims. A

motive force may be applied to an outside elemengt,.the output-being a function of the input.

. In the following specification show specific examples of practice according to my It will be understood that ;the specification relates largely to these particular cases and that the invention is defined in "Referring to.-the drawings, Figure 1 is a diagram of a transmission system embody v.ing my invention; Fig. 2 is a diagram showing phase and amplitude distortion as functions of frequency in several instances that be referred to in explaining the principle of will be referred to in this specification; Fig.

' 3 is a diagram of the apparatus P at the receiving end of the line L of Fig.- 1; Fig.4: is a diagram of a recurrent network that will my invention; Figs. 5 to 9 are diagrams .of alternative network sections that may be em- 1924. Serial No. 722,506.

ployed; Fig. 10 is an arrival curve diagram,

and Fig. 11 is a diagram showing a modifica- I tion.

Referring to Fig. l, the line L connects the transmitter T with thereceiver B, through the network Pwhose input impedance is R, but those internal structure is as yet undetermined. R equals the resistance .of the receiver R, which will be designed to be free from reactance. The line L retards the current components of difierent frequencies by different amounts and. also attenuates these components differently, and apparatus P is interposed at the receiving end to compensate the resultantdistortion on the line, so that the received wave form shall be the same as at the transmitting end.

As an example to illustrate the nature of my invention, let it be assumed that the line I L is a submarine cable of length 1,700 miles, whose constants are Resistance 1==2.74 ohms per mile Inductance L= 0.001 henrys per mile; Capacity C=0.296 microfarads per mile.

Also let it be assumed that and that the compensation is to be made over the range from 0 to 25 cycles per second.

In Fig. 2 the scale of ordinates gives napiers for attenuation and radians for phase. The curve a. gives the absolute value, expressed in napiers as a function of frequency,

of the ratio of voltages at the transmitting and receivin ends of the 1,700 mile cable which is terminated by apparatus P of impedance R, and the curve Z2 gives the corresponding value of phase retardation in radians as a function of frequency.

Instead of the characteristics. a and b, it would be an ideal state of affairs if the characteristic for the attenuation were a horizontal straight line such as a, and if the characteristic for the phase were a straight line through the origin, such as b. This would mean that the attenuation was constant over the frequency range involved and that the phase retardation, measured in radians, was proportional to the frequency, which is equivalent to zero displacement of the various frequencies relatively to one another. The

ideal characteristics a and 6 could obviously be obtained for the voltageacross the receiver R- if the line were supplemented by a network having the characteristicsjA and B when terminated as it is by the receiver R of impedance R. It may be more practicable to get the complete desired phase adjustment in aseries of sections instead of in a network of a single section, and in the case of a plurality of sections, it will be convenient, but not necessary, to have them alike and essential to have them so designed'that there will be no objectionable reflection efliects betwcen them.

In Figs. 5, 6,7, 8 and 9, respective network sections are shown, each of them except Fig. 9 comprising one or more resistance elements R (or simple multiples or sub-multiples of R) and all having unknown impedances a and 2 In all of these figures the condition is imposed that i then the characteristic impedance at all fre quencies will be equal to R. For example, taking the characteristic impedance in such 'case as an unknown quantity and calling it Z, we have the admittance equation for Fig. 6

This has a solution independent of 2 and 2' namely, Z =R, and it can be proved similarly for the other Figs. 5 to 9 that when repeated to infinity, they have the characteristic impedance R. In the ease of the unsymmetrical sections of Figs. 5 and 6 this applies only to the characteristic impedance from left to right; I call these five networks in orderv by the titles full-series, full-shunt, mid-series, mid-shunt, and lattice constant R networks.

The propagation constants of these networks are dependent upon the form of 2, and through Equation (1) on the form of 2 It can readily be shown by ordinary means that for Figs. 5, 6, 7 and '8 the current ratio per section of the infinite structure, expressed in terms of the propagation constant I, is given 7 6 1 2T?! whence I z /R=e 1.

For Fig. 9 the current ratio, similarly obtained, is s er=1 +z11/R., I

' Zn/R tanh Hence, the propagation constant I andthe impedance ratio z /R are mutually dependent in accordance with the above relations,

tively simple one of determining the locations and magnitudes of impedance elements in a which over the desired frequency range have approximately the prescribed impedance characteristics.

.Therefore, by making the network P of Fig. 1 of a series of sections like any one of Figs. 5 to 9, with R arbitrarily chosen, in'this case 'JL/C, it is assured that the network will have the impedance B at all frequencies provided it is suitably terminated at its output end by any network or receiver of resistance R as shown in Fig. 4. The voltage across the input terminals of network P is then independent of the networks transmitting properties and is the same as would be at the receiver if P were omitted entirely. In order to obtain the desired voltage across the receiver it remains to determine the specific design of 2 and 2 and-the number of sections' so that the attenuation and phase characteristics of the network correspond to the curves A,, and B of Fig. 2.

In the particular case now under consideration by way of example, I choose the network section of Fig. 6. If n similar sections are assumed the propa ation constant per section shouldideally be or the frequency range considered terminates the cable (r, L, C) of length l as in the well known formula 2) ice) sinh'yl cosh'yl) e- (6) where 'y= ,(1'+iwL)'iwQ, k= 1/ WWW w t The ideal impedance ratio z /R=- +i aw must have resistance and reaetance components 1' and m determined by Equation (3) in which I has Thus t r NnIn (BID/ 11 i Sin p/ To first determine the structure for i 2,, choose some value of n which. will ensure merely that the propagation constant per secthe value of Equation (5 tion is within the limits physically demanded by Equation (7) to give-a positive'resistan'ce component r namely and cos (Bk/mil.

Here n 3 is satisfactory and the ideal resist- '10, ance component 1' "decreases from alarge value at zero-frequency to a small value at f =25- while the ideal reactance component m decreases from zeroat zero frequency to a minimum and then increases to zero at 13 f It will readily be recognized that a physh=a small assumed value a value of a at zero frequency a, value of a at zero f 'frequency f frequency at whlch B is a mlnlmum (B' ideal minimum phase The impedance expression for 2 is w z 12 11 1 1 11 11 R11 R12 i-(L1121rt 1/C112Tt) 3 5 whence and I 4 tan B 2 +1 1 The value of 0 comes from the relation at f and is Since h/'(a,, -.a is small, 6/ g will here always be small compared to unity and there- 75 fore the approximate result from Equation (16), 1+c= .e can be used in (15) wherealso powers of c/g are neglected. With these ical'impedance having approximately these. characteristics is that shown for ah in Fig. 3 Where a takes the form of a parallel combination having a resistance R on one side and the resistance R5, the inductance L and 1 the capacity C in series on the other side.

Having thus determined a possible'type of v strutcure for a we need to fix'the best number n of sections of this type and assign values to the elements of 2 which approximately give the ideal propagation constant. The form of a and the values of its elements are determined by Equation (1).- To obtain the five unknowns 1, R R L and C itis q V I c one relation between g-and n. Another relation can be found from the requiredminimum phase (BQ/n); at f At this minimum A dB T so that by Equations (10) and (12) approximations, the second relation between g and a becomes from Equation (15) ten pl mi "g /2(y+ The elimination of g between Equations (13) and (17) gives the vtranscendental equation specifyingn Owing to the fact that n must be an integer, the proper value for n, is that one which most nearly satisfies Equation (18).

To the same order of approximation as Equation (17), d from (14) is =9 '7 Ui lfmf (9 Hence, the unknown parameters are to be determined from the above equations in the following order n from Equation (18), g from Equation (13), c from Equation (16), d from Equation (19).

For the example under consideration the solution is Hence, from Equations (11) and (1) the particular values taken by the resistance and reactance elements of Fig. 3 are as follows:

R =58.1 ohms; R =8580 ohms; R =9.4 ohms;

L 1.99 henrys; G =20.3 microfa rads; R

2 0.39 ohms;

1 358 ohms;

, L 0.0685 henrys;

C 590 ,microfarads.

A, indicates. an approximately uniform attenuation for theline and network over the whole frequency range from 0 to 25 cycles per second. Above 25 cycles the characteristic turns decidedly upward, indicating greater attenuation for higher frequencies, which is obviously desirable when only the range below 25 cycles is to be utilized. The phase characteristic B corresponds approximately to a straight line through the origin most of the way from O to 25 cycles per second, wh'ch means that the phase measured in radian is substantially proportional to the frequency, and accordingly, any wave form will bereceived with its components within the range in substantially the same relationinor'der of time.

It remains to supplement the network described thus far with the amplifier indicated as m Letting m be the desired amplification per section of network, the total amplification is m because there are two such sections.

Fig. 10 shows the arrival curve for the line L at 1, and at 2 it shows the arrival curve for the combined line and network. The improvement due to the network is obvious.

A similar procedure can be carried out for the lattice structure (Fig. 9), based upon Equation (4). Or, if the ladder network in the form of Figs 7 or 8 is known, the corresponding lattice section can be derived by the aid of formulas given in my paper in the Bell System Technical Journal for January, 1923.

Instead of a separate amplifier as at m in Fig. 3, the sections of the network can be designed so as to afford the proper amplification within each section. This is illustrated in Fig. 11. The equation for the propagation constant 1 in any ladder type constant R network such as in Figs. 5 to 8 is given by Equation (3).

Now assume a network of the same type as in Fig. 3, except that it amplifies by the factor m. For this network we have the equation:

By reference to- Figsffi and 3, and with the 7 data for Fig. 3, the construction and details of Fig. 11 follows at once. The element represented by (-R), a negative resistance, may comprise one or more three-electrode vacuum tube amplifiers.

In the use of the terms impedance and resistance it will be advantageous to remember that for any frequency of alternating current the impedance is the ratio of electromotive .force to current, and that in general the impedance will be a vector which may be represented by a complex number; if this ratio is a real number, it means that the impedance is a pure resistance.

I claim: 1. In combination, a transmission line producing various phase displacements and various degrees ofattenuation for component currents of various frequencies, and a network connected with the line and producing compensating phase displacements and attenuations at the respective frequencies, whereby ducing'varioushase displacements andva rious degrees attenuation for component currents of various frequencies, and a series of network sections connected-with the line,

5 each producing partial-compensating phase displacements and attenuations at the respective frequencies, whereby the total compensation of the network neutralizes the distortion on the line, and the received current has 19 its components in the same phase relation and the same. relative magnltude as the transmitted current. q 4. A device havinga pair of input terminals and a pair of output terminals and adapted to distort a current through it in D respect to the phase relations of the different frequency components, said device consisting of at leastone sectionof constant R network subject to the relation z .e =R with 2 0 2 formed of impedance elements combined to give the desired phase distortion.

5. In combination, a transmissionline producing various phase displacements and various degrees ofattenuation for component cur- 2 rents of various frequencies, a constant B a network connected therewith to compensate phase displacements and attenuations at the respective frequencies, and. an amplifier to bring the compensated current up to the desired magnitude.

' 6.- The method of compensating for phase distortion and amplitude distortion in atransmission line, which consists in counterdistorting the currents received over the line both 3 for amplitude and phase distortion, and 1 thereafter keeping the ratio of electromotive force to current at a constant real number a value and also before such counterdistortion keeping the ratio of current to electromotive 40 force at the same constant real number value and thereby keeping the current after such counterdistortion with its components in the same phase relation as at the sending end and of: the same relative magnitude.

145 '7. .The method of compensating for distortion ina transmission lme, which consists I 1 i in plotting the angular retardation in radians and the attenuation in napiers against frequency for the various frequency components in the received current, drawing a straight line through the origin intersecting the retardation plot at the upper limiting frequency of the desired range, and-drawing another horizontal straight line,' these straight linesbeing ideal for retardation and attenuation characteristics, and affecting the received current fromthe line so as to. produce therein complementary retardations and attenuations at the various frequencies keeping the ratio of electromotive force to current as. constant real nuniber value .both before the current is so affected and thereafter, whereby the'output current fromthe network conforms approximately to the said. ideal characteristics. i

- 8. In combination, a transmission line for a composite electric current producin vari ous phase displacements and various egrees transmitter and a receiver associated with said line anda network also associated with the line and producing compensating phase displacements and attenuations at the respec-' of attenuation for component currents a. I

tional constant R network associated with the line and producing compensatingphase,

displacements and attenuations at the respec-. the frequencies wherebycthe current received over the combination ofthe line andnetwork has its components inthe same phase relation and the-same relative magnitude as the transmi-tted current.

- In testimony whereof, Ihave signed my June, 1924.-

name to this specification this 20th day of orro mzoisEL, 

